It is important in many electrical circuits that various current sources maintain stable and fixed current output relative to one another. In an example, a current steering digital to analog converter (DAC) includes a plurality of current sources. The relative mismatches between the current sources with varying operating conditions can directly affect linearity of the DAC. As used herein, a “current source” comprises an electrical circuit that delivers current (e.g., electric current), which is ideally independent of the voltage across it (i.e., the current source). In practice, current sources have non-idealities, such as finite internal resistance, which can cause the current source to deviate from ideal behavior. In general, active current sources may be implemented using active electronic components (e.g., transistors) having current-stable nonlinear output characteristics when driven by steady input current or voltage.
Mechanisms to decrease the mismatch between the various current sources can include a calibration technique that trims (e.g., calibrates, adjusts, regulates, etc.) all current sources to a reference current source using a trim circuit. In one example mechanism, the trim circuit includes a calibration DAC (CAL DAC), which injects a small correction current in parallel with the current source under calibration (or correction). The total current of the current source and the trim circuit is measured against a master reference current and the difference is forced to approach zero through a successive approximation register (SAR) logic circuit.
However, the output current generated by the CAL-DAC does not generally track environment changes, such as temperature and bias current changes. Bias current refers to a direct current (DC) that is made to flow between two points of an active electronic component for purposes of controlling its behavior. Assume that the current source comprises a metal oxide semiconductor field effect transistor (MOSFET), which can be either of NMOS type, or PMOS type. The bias current (I) to voltage (V) relationship of the current source follows a square law:
  I  =                              μ          ⁢                                          ⁢                      C            ox                          2            ⁢              W        L            ⁢                        (                                    V              GS                        -                          V              TH                                )                2              =                  β        ⁡                  (                                    V              GS                        -                          V              TH                                )                    2      where μ is the electron or hole mobility (depending on the transistor type), Cox is gate capacitance of the transistors, W and L are width and length, respectively, of the gate, VGS is the voltage between the gate and source of the transistor, and VTH is the threshold voltage. The current mismatch ΔI between the reference current source and the current source to be calibrated can be expressed as follows:
      Δ    ⁢                  ⁢    I    =                              Δ          ⁢                                          ⁢          β                β            ⁢      I        -                  g        m            ⁢      Δ      ⁢                          ⁢              V        TH            where
            g      m        =                  2        ⁢        μ        ⁢                                  ⁢                  C          ox                ⁢                  W          L                ⁢        I              ,is transconductance of the transistor. In a general sense, transconductance is a ratio of a current change at an output port of the transistor (e.g., MOSFET) to a voltage change at an input port of the transistor.
In general,
      Δβ    β    ,ΔVTH, I, and gm determine the current mismatch, where
      Δ    ⁢                  ⁢    β    βand ΔVTH are device mismatches (e.g., caused due to processing and other factors) between the current source under calibration and the reference current source. In general, gm is temperature and bias current dependent (e.g., because mobility μ is a function of temperature, and gm varies with the bias current). Therefore, the current mismatch as a function of I and T can be expressed as:
      Δ    ⁢                  ⁢          I      ⁡              (                  I          ,          T                )              =                              Δ          ⁢                                          ⁢          β                β            ⁢      I        -                            g          m                ⁡                  (                      I            ,            T                    )                    ⁢      Δ      ⁢                          ⁢              V        TH            
The full scale current (e.g., maximum value of current) of currently existing CAL DACs is only proportional to bias current I. The output of the CAL DAC is a portion of the full scale current based on a fixed (e.g., constant) scale factor. Usually the current source is calibrated under a certain environment, including a specific temperature and bias current. When the environment such as the bias current and temperature change, the output current of the CAL-DAC trim circuit does not track the current source mismatch. As a result, although the current source may be calibrated to match the master reference current, the calibration can become erroneous with changes in temperature or bias current; consequently, the current sources fail to maintain stable and fixed current output relative to one another. Recalibration of each current source would be required in the changed environment.